Preheat the oven to 350 degrees F. Generously butter a 9-inch fluted tart pan with a removable bottom.
Whisk the flour, baking powder and salt in a medium bowl. Beat the butter, peanut butter and both sugars in a separate bowl with a mixer until smooth. Beat in the egg and vanilla. Add the flour mixture and stir with a wooden spoon until combined.
Press half of the dough into the prepared tart pan. Spread the jam over the dough, leaving a 1/2 -inch border around the edge. Drop about half of the remaining dough over the jam by the tablespoonful; lightly press the rest of the dough into the pan around the edge to form a crust. Bake until golden, 45 to 50 minutes.
Transfer the pan to a rack and let cool. Remove the ring and transfer the tart to a plate.